Antonio Gramsci: En búsqueda de una práctica contra hegemónica

2.2 Zusatzinformationen zu oxidiertem Lumiflavin in

Wasser

Der folgende Abdruck1

„Supporting Material to the manuscript:

Density Functional Theory Combined with Molecular Mechanics: The Infrared Spectra of Flavin in Solution“

Benjamin Rieff, Gerald Mathias, Sebastian Bauer und Paul Tavan

enthält zusätzliche Informationen über die Betrachtungen der DFT/MM generierten IR Schwingungsspektren von oxidiertem Lumiflavin in Wasser, die nicht im Haupttext der ersten Veröffentlichung enthalten sind. Auf neun Seiten, gegliedert in 4 Abschnitte, stellt die Supporting Information insgesamt vier Abbildungen, sechs Tabellen, eine Gleichung und verschiedene Diskussionen bereit, die (i) das CHARMM22 ähnliche MM Kraftfeld für das Lumiflavin und das FMN, (ii) die Konsequenzen von unterschiedlich gewählten Lennard-Jones Parametern der Carbonylsauerstoffe auf die Solvatisierung sowie die IR Schwingungsspektren von Lumiflavin, (iii) die Bandenzuordnung und Isotopenshifts für weitere neun Schwingungsbanden des Lumiflavins und (iv) die Aussagekraft der zu Grun- de gelegten Gauss‘schen Modelle für die DFT/MM-INMA Spektren von Lumiflavin do- kumentieren und erklären.

1_{Mit freundlicher Genehmigung des Wiley Verlags. Kostenlos einsehbar unter DOI: 10.1111/j.1751-}

1097.2010.00866.x

Supporting material to the manuscript

Density functional theory

combined with molecular mechanics:

The infra-red spectra of flavin in solution

Benjamin Rieff, Gerald Mathias, Sebastian Bauer, and Paul Tavan∗

Theoretische Biophysik, Lehrstuhl f¨ur Biomolekulare Optik, Ludwig-Maximilians-Universit¨at, Oettingenstr. 67, 80538 M¨unchen, Germany

∗_{corresponding author, email: [email protected],}

1

CHARMM22 type force field for isoalloxazine

The CHARMM22 [1] force field does not cover the isoalloxazine moiety. Because we needed a corresponding parameter set for our MM-MD simulations of LF in aqueous solution, we had to generate such a set. As explained in Section Methods we carried out, for this purpose, DFT calculations on the isolated LF and DFT/MM calculations on LF in TIP3P and TIP4P water to determine many of the required parameters and applied homology modeling for the remaining ones. According to Figure S1 the results are given in the tables S1-S4.

Figure S1: Chemical structure and atom labels of isoalloxazine and a definition of labels for bonds (numbers) and angles (capital letters).

Fig. S1 uses the chemical structure of LF to introduce names for the atoms, labels for the bond lengths (integer numbers) and for the bond angles (capital letters).

atom type qg ql atom type qg ql

N1 NN3A −0.4291 −0.6632 C8 CA3 0.1146 0.1272 C2 CN1A 0.5123 0.7244 C9 CA4 −0.2497 −0.2561 O2 ON1 −0.4890 −0.6419 H9 HP 0.1968 0.2345 N3 NN2U −0.2315 −0.2509 C9A CPTA −0.1534 −0.1809 H3 HN2 0.2631 0.3129 N10 NN2G 0.3171 0.3518 C4 CN1B 0.2558 0.3368 C0A CN5A 0.0847 0.2462 O4 ON1 −0.4266 −0.5287 C7M CT3 −0.2709 −0.3123 C4A CN5B 0.3475 0.2929 H7x HAI 0.0903 0.1041 N5 NN3A −0.4759 −0.5408 C8M CT3 −0.3117 −0.3879 C5A CPTB 0.3114 0.3861 H8x HAI 0.1039 0.1293 C6 CA1 −0.2004 −0.2774 C0M CT3 −0.3078 −0.5520 H6 HP 0.1339 0.1647 H0x HAI 0.1026 0.1840 C7 CA2 0.1184 0.1621

Table S1: CHARMM22 atom types and partial charges calculated by DFT for isolated LF (qg) and by DFT/MM for LF in water (qg) are associated to the atom names defined in Fig. S1.

Table S1 associates certain atom types to the atom names defined in Fig. S1. In CHARMM22 S1

1 CHARMM22 TYPE FORCE FIELD FOR ISOALLOXAZINE

such types serve as selectors for force field parameters. The table extends the set of CHARMM22 standard types CN1, CN5, CPT, and CA by adding capital letters (A,B) or numbers (1,2,3,4) to uniquely define a certain positions within isoalloxazine. The table also contains partial charges applicable to LF in the gas phase (qg) or in water (ql). These charges were calculated by the

procedures described in Section Methods. Comparing the gas phase values |qg|with the liquid phase values _|ql|one recognizes a general increase, i.e. an enhanced polarity of the LF molecule.

CHARMM22 models the bond stretches, the angle deformations, and the stiffnesses of sp2

hybridized atoms by harmonic potentials specified by force constants and equilibrium values of the associated internal coordinates, which are the bond lengths li, the bond angles θj, and the so-called improper dihedral angles φk, respectively.

bondi kl[kcal/mol] l0[˚A] bondi kl[kcal/mol] l0[˚A]

1 300.2 1.384 15 384.4 1.090 2 749.1 1.227 16 326.7 1.405 3 185.1 1.420 17 300.2 1.388 4 472.2 1.024 18 295.7 1.392 5 310.3 1.386 19 265.9 1.508 6 767.6 1.225 23 265.0 1.507 7 187.6 1.503 27 249.1 1.470 8 463.5 1.307 20-22 359.4 1.100 9 284.9 1.370 24-26 359.4 1.100 10 346.1 1.409 28-30 359.4 1.100 11 379.9 1.092 31 425.9 1.312 12 327.0 1.388 32 295.0 1.461 13 315.6 1.426 33 311.6 1.425 14 354.0 1.396

Table S2: Force constants kl and equilibrium values l0 calculated by DFT for the isoalloxazine

bond lengths li, whose labels iare defined by the numbers in Fig. S1.

Table S2 lists the parameters calculated by DFT for the harmonic potentials of isoalloxazine’s bond lengths li. Table S3 displays the corresponding data for the bond anglesθj.

A dihedral angle φk is usually characterized by a label k denoting a set of four atoms. For the improper dihedrals φk used by us to ensure the planarity of isoalloxazine the labels k are listed in Table S4. All associated harmonic potentials have the same force constant kφ = 100 kcal/(mol_·rad2_{) and equilibrium value φ}

0 = 180◦.

The description of the isoalloxazine force field is complete, as soon as also the parameters of the Lennard-Jones (LJ) potentials are given. For these parameters we adopted the values specified in the CHARMM22 force field [1] for the basic atom types.

The LF molecule was extended towards FMN by attaching a glycerol chain and phosphate ion to atom N10 (cf. Fig. S1). The CHARMM22 force field provides a parametrization for these two

chemical motifs, which was adopted.

angle j kθ [kcal/mol rad2] θ0 [degrees] angle j kθ [kcal/mol rad2] θ0 [degrees] A 105.00 123.33 M 77.00 120.14 B 249.75 117.61 N 52.20 118.65 C 70.00 115.51 O 230.00 121.27 D 91.60 127.94 P 52.25 122.71 E 117.00 122.84 Q 422.50 120.99 F 81.00 112.44 R 70.00 120.17 G 33.60 118.60 S 70.50 120.61 H 250.00 118.13 T 81.25 120.16 I 75.00 118.86 methyl at CA2 38.00 110.10 J 53.75 116.62 methyl at CA3 38.00 110.10 K 220.70 122.20 methyl at NN2G 40.50 110.10 L 78.50 118.45 methyl H-C-H 35.50 108.40

Table S3: Force constants kθ and equilibrium valuesθ0 calculated by DFT for the isoalloxazine angles θj, whose labelsj are given by the capital letters in Fig. S1.

labelsk of improper dihedralsφk labelskof improper dihedralsφk

ON1 NN3A CN1A NN2U CPTB NN3A CA1 HP

NN3A CN1A NN2U HN2 NN3A CPTB CA1 CA2

CN1A NN3A NN2U CN1B CA1 CPTB CA2 CA3

CN1A NN2U CN1B ON1 CA2 CA1 CA3 CA4

NN2U CN1A CN1B CN5B CA2 CA3 CA4 HP

NN2U CN1B CN5B NN3A CA3 CA2 CA4 CPTA

CN1B CN5B NN3A CPTB CA3 CA4 CPTA NN2G

CN5B NN3A CPTB CA1 CA4 CPTA NN2G CN5A

Table S4: The labelskof the improper dihedral anglesφk, which are employed to guarantee the planarity of isoalloxazine, are quadruples of atom types pointing to the four atoms, which are harmonically forced to be coplanar.

2

Choice of Lennard-Jones potentials.

In a microscopic description of a solvent surrounding a molecule one explicitly includes the van der Waals interactions. In addition to the electrostatics, also these interactions affect the solvent’s short range order characterized by Fig. 6 for the neighborhood of the flavin carbonyl groups. This insight leads to the question, to what extent the solvation patterns are influenced by the choice of the LJ parameters for the carbonyl oxygens.

Steering the carbonyl solvation. We checked this parameterization issue by calculating

additional INMA spectra of LF in TIP3P and TIP4P water using altered LJ parameters for the LF oxygen atoms O2 and O4. Here we slightly increased the van der Waals radii from 3.0291

˚

A to 3.1538 ˚A and the depths of the LJ potentials from 0.1200 kcal/mol to 0.1521 kcal/mol. In CHARMM22 [1] the former values belong to atom type ON1 and the latter to ON5 (in guanosine, e..g., ON1 models the carbonyl and ON5 the hydroxyl oxygen atoms). Depending on the solvent model, DFT/MM spectra obtained for the modified LJ potentials will be labeled by T3LJ and T4LJ, respectively. To assess the steering of the solvation, we have first calculated the

radial distribution functions gOH(r) of the TIP3P hydrogen atoms around the modified models

2 CHOICE OF LENNARD-JONES POTENTIALS.

of the LF oxygen atoms O2 and O4 from a 1 ns MM-MD simulation.

Figure S2: Radial distribution functions gOH(r) of the TIP3P hydrogen atoms surrounding

the flavin oxygen atoms O2 and O4 using standard (solid lines) and altered (dashed lines) LJ

parameters.

Figure S2 compares the distribution functions gOH(r) for the standard (solid lines) and mod-

ified (dashed lines) LJ models of the carbonyl oxygens O2 and O4. The graphs immediately

demonstrate for each of the two carbonyl groups that the larger van der Waals radii of the flavin oxygens assumed in the modified parameterization (dashed lines) shift the distancesrmaxof the

first maxima to larger values. Furthermore, the number of hydrogen atoms in the first solvation shell is found to decrease by 5 % at O2 ( from averages 2.56 to 2.43) and by 8 % at O4 (from

averages 2.28 to 2.09). The consequences of the correspondingly weakened solvation of the two LF carbonyl groups on the calculated IR spectra will now be scrutinized. One expects, of course, that this weakened solvation causes a blue shift of the carbonyl bands.

DFT/MM frequencies for modified Lennard-Jones parameters. Figure S3 compares

the DFT/MM vibrational frequencies of our five LF marker bands, which were obtained using the standard LJ parameters at the carbonyl oxygens (left part) and two solvent models (T3, T4), with the corresponding frequencies calculated by applying the modified parameters (right part) and the two solvent models (T3LJ, T4LJ). The central column (H2O) of Fig. S3 are

the experimental consensus data from Fig. 5. For a simplified visual comparison with these experimental data, all DFT/MM frequencies have been scaled by the factor 1.0334. This factor has been chosen as to minimize the RMSD of the four average DFT/MM frequencies hνC=Oi from the corresponding average experimental frequency.

Up to the scaling of the DFT/MM frequencies, the columns T4, T3, and H2O in Fig. S3 contain

the same data as the corresponding columns in Fig. 5. Thus the patterns of band shifts induced by exchanging the mildly (T4) by the strongly (T3) polar solvent model are essentially identical in the two figures. If one now increases the van der Waals radii of the LF carbonyl oxygen atoms and, thus, applies the weaker solvation characterized by Fig. S2 to the two carbonly groups, the DFT/MM calculations predict the expected blue shifts of the cabonyl frequencies for both solvents (cf. columns T3LJ and T4LJ in Fig. S3). In the case of the TIP4P water model

the average carbonyl stretching frequency hνC=Oi is blue shifted by 16 cm−1 and for TIP3P by S4

Figure S3: DFT/MM frequencies calculated by INMA for LF in liquid water using different models and scaled with a factor of 1.0334 are compared with the experimental consensus fre- quencies “H2O” for fully oxidized flavins in water (see Fig. 5). The scaled DFT/MM results

cover the data already shown in Fig. 5 in an unscaled fashion, which were obtained for LF in TIP3P (T3) and TIP4P water (T4) with the standard LJ parameters of CHARMM22 for the carbonyl oxygens. Furthermore, they cover frequencies obtained for the modified LJ parameters and for LF in TIP3P (T3LJ) and TIP4P water (T4LJ).

10 cm−1 by the increased van der Waals radii. In contrast, the average frequencieshνC=Niof the three C=N marker bands are nearly invariant (_±2 cm−1) upon the change of the LJ potentials at the carbonyl oxygens for both solvents. Thus, a modification of the LJ potentials at the carbonyl oxygens can be used to tune the spectral gap between the C=O and C=N modes. Furthermore, such a modification apparently has only minor effects on the spectral spacings among the C=N modes.

In contrast, the spectral gap ∆νC=O between the two high frequency carbonyl modes can be modified somewhat more strongly by the change of the LJ potentials. In the TIP3P case, for instance, the gap ∆νC=O decreases by 29 % [from 41 cm−1 (T3) to 29 cm−1 (T3LJ)], whereas

for TIP4P it increases by 7 % [from 27 cm−1 (T4) to 29 cm−1 (T4LJ)]. As compared to the

experimental value of 43 cm−1 for the gap, however, solely the original T3 model furnishes a reasonable description (41 cm−1). Therefore, we decided to consider the T3 combination of the TIP3P water model with the standard CHARMM22 parameters for the LJ potentials of the LF carbonyl oxygens as the most promising choice for the DFT/MM description of the IR spectra of flavins in solution or protein environments.

There are, most probably, better choices for the solvent model and for the LJ parameters of flavin dyes in DFT/MM calculations of condensed phase IR spectra. However, a systematic search for an optimal parameterization is excluded by the enormous computational cost posed by any such attempt. Here, we solely wanted to check to what extent two reasonable choices of LJ potentials for oxygen atoms, which are used in the CHARMM22 force field [1] for different chemical motifs, can modify spectral descriptions in a DFT/MM setting and whether, by chance,

3 ASSIGNMENT AND ISOTOPIC SHIFTS OF ADDITIONAL FLAVIN BANDS

we might detect a better description than the CHARMM22 standard, which is T3.

3

Assignment and isotopic shifts of additional flavin bands

Here we present additional data on flavin bands in the spectra region between 1200 cm−1 _and

1750 cm−1 . Table S5 shows IR frequencies for solid state LF dried on KBr discs together with a PED assignment based on an empirical normal mode analysis [2]. These data are compared with our scaled (1.031) DFT/MM-INMA frequencies and PED values, derived from the MT/BP normal mode analysis of the isolated LF by using the program Gamess [3].

No. exp/cm−1 PED T3/cm−1 PED

81 1708 61 νC4=O 20 νC2=O 1700 79 νC4=O 4 νC2=O 80 1662 82 νC2=O 16 νC4=O 1659 77 νC2=O 7 δN3H 79 1621 31 νC5AC9A 15 νC4AN5 1652 17 νC6C7 17 νC5AC6 78 1583 29 νN1C0A 19 νN10C0A 1580 31 νC4AN5 18 νC0AN1 77 1552 33 νN1C0A 18 νC4AN5 1559 32 νC7C8 18 νC0AN1 76 1513 33 νC4AN5 14 νC9AN10 1524 57 νC0AN1 40 νC4AN5 68 1461 20 νC7C8 15 νC8Me 1451 18 νC8C9 5 νC5AC6 64 1425 29 νC7C8 23 νC6C7 1409 35 νC8C9 15 νC7C8 63 1413 71 δN3H 8 νC4=O 1411 65 δN3H 9 νC4=O 62 1396 33 νC2N3 33 νC2N1 1382 20 νC7C8 12 νC4C4A 61 1346 17 νC5AC6 16 νN10C0A 1353 13 νN10C0A 10 νC4C4A 60 1301 30 νN5C5A 14 νC8C9 1312 32 νN10C0A 7 νC0AN1 58 1272 22 νC4AC0A 17 νC4N3 1288 49 δCH 11 νN5C5A 57 1238 43 νC4N3 23 νC4C4A 1236 24 νC4N3 17 νC8CM e

Table S5: IR frequencies (exp) observed for solid LF in a KBr disc and assigned by an empirical normal mode analysis to PED’s [2] (left) are compared with our scaled DFT/MM-INMA (T3) frequencies of LF and the PED associated to the MT/BP normal modes calculated for the isolated LF. Only the two largest local contributions to a normal mode are given in % .

To illustrate the normal mode compositions we calculated in addition to the PED also DFT/MM- INMA isotopic band shifts for the isotope labels enumerated in the caption to Fig. 9 (omitting, however, the deuterated case and all marker modes). Table S6 compares the isotopic band shifts calculated for LF in TIP3P water with IR data [2, 4] on solid state LF and with RR shifts measured for FAD in water [5].

The mode compositions of the five marker bands α = 81, 80, 78, 77, and 76 are extensively discussed in the paper. At this point we, therefore, solely add a few remarks on the character and compositions of some of the remaining 9 modes additionally covered by the Table S6. According to our DFT/MM results the modes 75-69 and 67-65 are dominated by methyl deformations, which carry mostly negligible intensities. The corresponding bands were experimentally not determined and, therefore, these modes are not listed here.

Inspecting Table S6 clearly demonstrates that the calculated level shifts nicely agree with the observed ones. If we choose as experimental reference, whenever possible, the average shifts resulting from the IR and RR experiments we find that our calculated shifts deviate from the observed shifts by an RMSD of only 2.9 cm−1. This value is well within the limits of the

No. native 13C2 13C4,0A 15N1,3 15N5 cm−1 T3 IR RR T3 IR RR T3 IR RR T3 IR RR 79 1652 0 0 ₋1 ₋2 0 0 ₋1 0 0 ₋1 68 1451 ₋2 ₋2 ₋1 ₋5 ₋3 ₋5 ₋1 ₋2 ₋1 ₋2 ₋2 ₋1 64 1409 −3 0 −3 −6 0 0 0 63 1411 0 0 −3 −2 −1 0 62 1382 ₋5 ₋13 ₋1 ₋8 ₋2 ₋4 ₋12 ₋2 ₋1 ₋1 0 61 1353 −5 −6 −2 −12 −12 −8 −2 −2 0 −2 −2 +1 60 1312 −1 −1 −6 −4 −1 −3 −3 58 1288 ₋2 ₋3 ₋2 ₋4 ₋1 ₋1 ₋2 ₋4 57 1236 0 −11 −4 −4 −3 −8 −9 −1 −2 +1

Table S6: Comparison of scaled DFT/MM and experimental frequencies representing IR [2, 4] and RR [5] data for native and isotopically labeled flavins. The column labels 13_C

2, 13C4,0A,

15_N

1,3, and 15N5 indicate the isotopic substitutions. The column ”native” repeats the scaled

INMA results of the T3 ensemble. The data for the five marker bands are omitted here, because they are displayed in Fig. 9.

experimental uncertainty, because the RMSD between the isotopic shifts determined by IR and RR, respectively, is 4.5 cm−1.

Also the details of our band assignment agree very well with the observed isotopic shifts. Con- sider, for instance, mode 79. Applying an empirical normal mode analysis Abe and Kyogoku [2] calculated PEDs (see Table S5), which indicate that this mode is mainly a mixture of the C5A-C9Aand C4A=N5stretching vibrations. In contrast, our DFT (and DFT/MM) calculations

assign only C-C stretches localized in ring I of isoalloxazine but no contribution of the C4A=N5

stretch to mode 79. Our result is consistent with the spectroscopic data for the isotopic substi- tution at N5. In agreement with our DFT/MM result, experimentally this substitution induces

shifts of at most 1 cm−1. If mode 79 would contain a substantial contribution of the C4A=N5

stretch, then one would expect a larger effect of this particular isotope substitution. Thus, for this mode our DFT(/MM) based normal mode analysis provides a more realistic description of the mode compositions than the quoted empirical normal mode analysis.

We leave it to the reader to compare for some of the other modes the details of the observed and calculated isotopic shifts with the predicted mode compositions. Admittedly, we cannot explain some of the discrepancies between the RR and IR data, which are most strikingly visible for mode 62 and may be due to the different experimental conditions with RR referring to aqueous solution and IR to the solid state.

4

Gaussian approximation for IR line shapes obtained by INMA

Eq. (9) assumes Gaussian shapes for the inhomogeneously broadened IR bands of flavin in solution. To check this assumption Fig. S4 compares three different representations of the INMA results on the IR spectrum of LF in TIP3P water.

4 GAUSSIAN APPROXIMATION FOR IR LINE SHAPES OBTAINED BY INMA

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